Bifurcation and Isochronicity at Infinity in a Class of Cubic Polynomial Vector Fields
Source: Acta Mathematicae Applicatae Sinica, Volume 23, Number 3, July 2007 , pp. 451-466(16)
Abstract:In this paper, we study the appearance of limit cycles from the equator and isochronicity of infinity in polynomial vector fields with no singular points at infinity. We give a recursive formula to compute the singular point quantities of a class of cubic polynomial systems, which is used to calculate the first seven singular point quantities. Further, we prove that such a cubic vector field can have maximal seven limit cycles in the neighborhood of infinity. We actually and construct a system that has seven limit cycles. The positions of these limit cycles can be given exactly without constructing the Poincaré cycle fields. The technique employed in this work is essentially different from the previously widely used ones. Finally, the isochronous center conditions at infinity are given.
Document Type: Research Article
Publication date: July 1, 2007